## Dynamics generated by finitely generated subgroups of conformal germs

- Generic subgroups of are non-solvable.
- Dynamics generated by several germs. Definition of a pseudogroup. Orbits of points.
- Periodicity of germs (finiteness of order) vs. periodicity of orbits. Cycles and limit cycles of pseudogroups.
- Convergence of elements in pseudogroups. Closure.
- Density of orbits. Linear subgroups. Abundance of limit cycles for generic (nonsolvable) subgroups of .
- Topological equivalence of subgroups and pseudogroups. Conjugacy of dense linear subgroups.
- Rigidity of nonsolvable subgroups: topological conjugacy implies holomorphic conjugacy.

Disclaimer… if somebody still needs it… 😦

Reading: Section 6 (second part) from the book, printing disabled.

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In the definition of a cycle (Def. 6.31) nontriviality of an element probably needs a clarification: in a (pseudo)group generated by

non-identical germsan element isnontrivialif it corresponds to a nontrivial word in the free group in symbols. Thus the identical germ is nontrivial if and only if admits nontrivial identities.Comment by Sergei Yakovenko — Wednesday, December 19, 2007 @ 4:52 |